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Wednesday, April 29, 2015

Early last week a news story broke about a supervoid. The supervoid was claimed to be a number of things, from an explanation for "the cold spot", to the biggest "structure" yet found in the universe, to just "mysterious".

Whether it is a structure or not entirely depends on how you define structure, so I won't discuss whether it is or isn't a structure. However, if you do allow it to be a structure, it isn't the biggest structure yet found. It's hard to do a like for like comparison with other "superstructures". However, there are regions of the universe where the density of observable matter is smaller, for a wider range, so by any definition I can think of, this structure has been beaten.

The cold spot is a region in the cosmic microwave background (CMB) that has a temperature profile that is somewhat unexpected (due to a combination of a cold central spot and a hot ring around it). Whether this void could be the explanation of the cold spot has been explained in this paper and this blog post by Sesh. It can't, not without a significant deviation from General Relativity (and a sufficiently big deviation that it would be very strange that these deviations haven't been seen elsewhere). It's worth stressing right now that it isn't the coldness of the cold spot that is itself anomalous. This is a subtle point so just about anyone who says "the cold spot is too cold" can be forgiven for the mistake, but in reality the cold spot isn't too cold. In fact it has more or less exactly the coldness expected of the coldest spot in the CMB. What isn't expected is that there will be a hot ring around such a cold spot. Actually, it's worth stressing further that it isn't even the hot ring that is, by itself, anomalous. Such a hot ring is also quite likely in the CMB. The anomalousness of the cold spot is caused by the fact that both of these features are present, right next to each other. I explained this curiosity in this blog entry, but it is worth repeating.

I want to address now quickly the claim that this supervoid is mysterious. The quantitative source for the claim that the void is mysterious comes from the claim in the paper about the void that it is "at least a \(3.3 \sigma\) fluctuation" and that "\(p=0.007\) ... characterizing the cosmic rarity of the supervoid". However (and this is the crucial point) what these numbers quantify is the probability that something as extreme as this void could exist at a random point of the universe (or, more precisely, a random point within the part of the universe seen by a particular observational survey). What these numbers do not quantify is the probability that the whole survey could have seen something this extreme. These are two separate statistical things and the relevant one for claiming mysteriousness is the second one. I'll try to estimate this probability.

I don't have any reason to doubt the numbers they quote for the probability that this void could exist at a random line of sight in the survey. If I use the quoted radius, density contrast and redshift of the void I also calculate it to be a \(\sim 3\sigma\) fluctuation in the matter field. This can be done first by calculating the root-mean-square of the density (contrast) field of the universe when it is smoothed over a particular radius. This quantity, "\(\sigma_R\)", is commonly used in large scale structure. Then, the ratio of the density (contrast) of the obtained void and the \(\sigma_R\) value for the radius of the void gives you \(\sim 3.5\) so I trust that the more sophisticated analyses in the paper are correct, or at least aren't obtaining wildly wrong answers. If one assumes (probably validly) that the large scale density field of the universe has a Gaussian distribution this can be translated into a probability that the observed fluctuation could occur at any random position in the universe.

So, the crucial question that now needs to be asked before calling this supervoid mysterious is whether the survey used to find it saw enough of the universe to witness this rare an event. The size of the void in the sky is approximately \(10\) degrees (as quoted in their abstract). This means it has an area of approximately \(100\) square degrees on the sky. The void was found using data from the WISE and 2MASS all-sky surveys. However the whole sky isn't usable for robust analysis due to foregrounds, the galaxy, etc. Thankfully for our goal, the authors of the supervoid paper also wrote a paper about the catalogue of galaxies they used to find the supervoid and in the abstract of that paper they estimate that their catalogue covers 21,200 square degrees of the sky.

What does this mean when we pull it all together? Well, the catalogue used to find the 100 square degree thing, covered 21,200 square degrees of the sky. Therefore, there were \(\sim 21200/100 \simeq 200\) independent \(100\) square degree patches of the sky seen by the survey. Using their own probability for this void existing at any particular line of sight of \(p=0.007\) this gives a very approximate estimate of the expected number of under-dense regions of the universe at least as extreme as the "mysterious" supervoid. The answer is \(N \sim 200*0.007 = 1.4\).

So, not only is the supervoid not actually mysterious, it is in fact more or less exactly in line with naive expectations!